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Chapter 3: Problem 70

Graph. $$ y=\frac{3}{2} $$

Short Answer

Expert verified
The graph is a horizontal line at y = \( \frac{3}{2} \).

Step by step solution

01

Understand the Equation

The given equation is a horizontal line where the value of y is constant for all values of x. In this case, y is always equal to \( \frac{3}{2} \).
02

Identify Key Points

Since y is always \( \frac{3}{2} \), select any values for x. For example, x = -2, x = 0, and x = 2.
03

Plot the Points

Plot the points (-2, \( \frac{3}{2} \)), (0, \( \frac{3}{2} \)), and (2, \( \frac{3}{2} \)) on a graph.
04

Draw the Line

Connect these points to form a horizontal line. This line represents the equation \( y = \frac{3}{2} \).
05

Check the Line

Ensure that the line is horizontal and passing through y = \( \frac{3}{2} \) for all x-values.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

coordinate plane
To understand graphing, we start with the coordinate plane. This plane is a two-dimensional surface defined by two perpendicular lines: the x-axis (horizontal) and the y-axis (vertical). Each point on the coordinate plane is determined by a pair of numbers called coordinates (x, y). The first number, x, indicates how far left or right the point is from the origin (0,0), while the second number, y, indicates how far up or down the point is from the origin.

For example, the point (3, 2) is 3 units to the right of the origin and 2 units up. Knowing how to interpret and use the coordinate plane is essential for plotting points and graphing functions.
constant function
A constant function is a function that always returns the same value, no matter what the input is. In mathematical terms, it's written as y = c, where c is some constant number. For the exercise, the function is y = \(\frac{3}{2}\), which means regardless of the x-value, y will always be \(\frac{3}{2}\).

This type of function is interesting because it produces a horizontal line on the coordinate plane. Horizontal lines are simple because their slope is zero. Understanding constant functions helps in recognizing patterns and forming a strong foundation for more complex graphing.
plotting points
Now, let鈥檚 talk about plotting points, which is a key step in graphing the function. To plot a point, you need a pair of coordinates (x, y). Here's the process:

  • First, locate the x-coordinate on the x-axis.
  • Next, find the corresponding y-coordinate on the y-axis.
  • Finally, mark the point where these two coordinates meet.

For the given exercise, we plot the points (-2, \(\frac{3}{2}\)), (0, \(\frac{3}{2}\)), and (2, \(\frac{3}{2}\)). All these points will lie on the horizontal line representing y = \(\frac{3}{2}\). Connecting these points, you end up with a straight horizontal line.

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